Alumina ceramic material - Mat110 : should it be coupled with EOS ?

[GearDyn 1]

Hello all, 

i'm modelling a ballistic impact on Alumina ceramic targets , & will be utilising  Mat 110  ( reference journal  as shown below).... 

Query is , should we use EOS while using this material? if so , which EOS is better 

Also if the unit consistency is changed , where to get the conversion factors for the parameters ? 

  mm s

Reference Journal : Steel spheres impact on alumina ceramic tiles: Experiments and finite element simulations : Genevieve Toussaint

(https://www.researchgate.net/publication/333938585_Steel_spheres_impact_on_alumina_ceramic_tiles_Experiments_and_finite_element_simulations)

thanks in advance

[James Kennedy]

Dear GearDyn,

 

In LS-DYNA, MAT_110 (also known as MAT_STEINBERG_HY) is a material model designed for simulating elastic-plastic, hydrodynamic materials under extreme conditions, such as high strain rates and shock waves. It requires a separate equation of state (EOS) to define the pressure-volume-internal energy relationship of the material. The coupling of MAT_110 with an EOS is what allows for accurate modeling of these high-pressure, high-strain-rate phenomena. 

 

The role of an EOS with MAT_110 

 

MAT_110 calculates the material's deviatoric stress, which is its strength behavior.

 

The separate EOS calculates the hydrostatic (or bulk) pressure, which is the volume-dependent part of the stress.

 

The total stress is the sum of the deviatoric stress from MAT_110 and the pressure from the selected EOS. 

 

Common equations of state used with MAT_110 

 

While any compatible EOS keyword can be used, the Gruneisen EOS is the most common choice for modeling solids with MAT_110 under shock compression. Other options include: 

 

EOS_GRUNEISEN: A popular choice for modeling the hydrodynamic behavior of metals and other solids under shock loading.

 

EOS_LINEAR_POLYNOMIAL: A more general-purpose EOS that can be used for a wide range of materials. For low to moderate strain rates, it can approximate the material's bulk modulus.

 

EOS_TABULATED: This option allows you to define the pressure-volume relationship via a user-defined table, offering maximum flexibility. 

 

Input for an EOS in LS-DYNA 

 

The specific input parameters depend on the chosen EOS. For example, to define the Gruneisen EOS, you would use the *EOS_GRUNEISEN keyword with parameters like: 

 

Reference density (𝜌0)

 

Sound speed in the material (𝐶)

 

Dimensionless material coefficients (S1,S2,S3)

 

Gruneisen gamma (𝛾0)

 

Correction term (𝑎)

 

This information is typically defined on a separate card following the *MAT_110 material properties. 

 

When to use an EOS with MAT_110 

 

The use of an EOS is essential when simulating phenomena involving: 

 

High-velocity impacts: A projectile impacting a target at high speed.

 

Shock wave propagation: Explosions or other events that cause high-pressure shock waves.

 

High strain rates: Deformations at rates exceeding 10^5 per second.

 

Pressure-dependent material behavior: Materials where the bulk pressure significantly affects the yield strength. 

 

Sincerely,

James M. Kennedy

KBS2 Inc.

August 27, 2025

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[James Kennedy]

Hello all, 

--

[James Kennedy]

Dear GearDyn,

 

Some links you might study for unit conversion

 

https://www.dynasupport.com/howtos/general/consistent-units

 

unit conversion ls dyna calculator

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[GearDyn 1]

Thanks James for the insights ,

but when i'm trying to include EOS , im getting the error which says Mat110 does not need EOS. 

But when the EOS is removed , the calc run perfectly

Thanks in advance, Harsha

[James Kennedy]

Dear GearDyn,

 

My apologies, my search engine failed me. MAT_110  and MAT_010 appear to have got mixed somehow.  

 

Notes from the following link indicates that no EOS is requireD for MAT_110

 

https://lsdyna.ansys.com/dynamat/#:~:text=This%20is%20Material%20Type%2010,of%20state%20determines%20the%20pressure.

 

MAT_­011

*MAT_­STEINBERG

HY, MT

FAIL, EOS, TEF, TC

This is Material Type 11. This material is available for modeling materials deforming at very high strain rates (> 10^5 per second) and can be used with solid elements. The yield strength is a function of temperature and pressure. An equation of state determines the pressure. This model is applicable to a wide range of materials, including thos with pressure-dependent yield behavior. In addition, the incorporation of an equation of state permits accurate modeling of a variety of different materials. The spall model options permit incorporation of material failure, fracture, and disintegration effects under tensile loads.

 

*MAT_­110

*MAT_­JOHNSON_­HOLMQUIST_­CERAMICS

CR, GL

SRE, FAIL, DAM, TC

This is Material Type 110. This Johnson-Holmquist Plasticity Damage Model is useful for modeling ceramics, glass and other brittle materials. A more detailed description can be found in a paper by Johnson and Holmquist [1993].

 

JH-2 primary references:

 

Johnson, G.R., and Holmquist, T.J., "An Improved Computational Constitutive Model for Brittle Materials", High-Pressure Science and Technology - 1993, American Institute of Physics, Vol. 309, pp. 981-984, July, 1994.

 

Johnson, G.R., and Holmquist, T.J., "Response of Boron Carbide Subjected to Large Strains, High Strain Rates, and High Pressures", Journal of Applied Physics, Vol. 85, No. 12, pp. 8060-8073, June, 1999.

 

Sincerely,

James M. Kennedy

KBS2 Inc.

August 29, 2025

[Emin Akca]

Hi,

*MAT_110 is the material model known in the literature as Johnson-Holmquist-II, which is an improved model from a previous one. The original model was JH-1, which is *MAT_111 in LS-DYNA. 

EoS is mathematical model for shock phenomena within materials. In simple terms, EOS determines the relationship between pressure, volume and temperature within the material experiencing shock waves. For a simple interaction, you should check Hugoniot and EoS chapters (Chapters 3.5 and 3.6) of the famous Studies in Applied Mechanics Vol.49: Introduction to Hydrocodes written by Jonas A. Zukas. 

You cannot use EoS with *MAT_110 or *MAT_111, as you experienced, LS-DYNA results in an error stating that those models do not require EOS. As jmk shared, you should read and understand the original papers written by Johnson and Holmquist in 1992 (JH-1) and 1994 (JH-2). Those models already have their built-in shock Hugoniot routines within their constitutive equations.

Best,

–Emin

[James Kennedy]

Dear Emin,.

 

*MAT_241 or *MAT_JOHNSON_HOLMQUIST_JH1

 

This is Material Type 241. This Johnson-Holmquist Plasticity Damage Model is useful for modeling ceramics, glass and other brittle materials. This version corresponds to the original version of the model, JH1, and Material Type 110 corresponds to JH2, the updated model.

 

The main difference between JH1 and JH2 models is that the JH2 model incorporates a mechanism of gradual increase of bulking pressure as the damage accumulates. The value of the bulking pressure depends on the fraction of internal energy loss converted to potential hydrostatic energy.

 

The advantage of the JH1 model is the model parameters can be determined in a more straightforward manner than the JH2 model.

 

JH-1 primary references

 

Johnson, G.R., and Holmquist, T.J., "A Computational Constitutive Model for Brittle Materials Subjected to Large Strains, High Strain Rates and High Pressures", EXPLOMET 90 International Conference on Shock-Wave and High-Strain-Rate Phenomena in Materials, San Diego, California, August, 1990.

 

Johnson, G.R., and Holmquist, T.J., "A Computational Constitutive Model for Brittle Materials Subjected to Large Strains, High Strain Rates and High Pressures", Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Meyers, M.A., Murr, L.E., and Staudhammer, K.P., Marcel Dekkar Inc., New York, New York, pp. 1075-1081, 1992.

 

Holmquist, T.J., and Johnson, G.R., "Response of Silicon Carbide to High Velocity Impact", Journal of Applied Physics, Vol. 91, No. 9, pp. 5858-5866, May, 2002

 

*MAT_110 or *MAT_JOHNSON_HOLMQUIST_CERAMICS  (JH-2)

 

This is Material Type 110. This Johnson-Holmquist Plasticity Damage Model is useful for modeling ceramics, glass and other brittle materials. A more detailed description can be found in a paper by Johnson and Holmquist [1993/1994].

 

JH-2 primary references

 

Johnson, G.R., and Holmquist, T.J., "An Improved Computational Constitutive Model for Brittle Materials", High-Pressure Science and Technology - 1993, American Institute of Physics, Vol. 309, pp. 981-984, July, 1994.

 

Johnson, G.R., and Holmquist, T.J., "Response of Boron Carbide Subjected to Large Strains, High Strain Rates, and High Pressures", Journal of Applied Physics, Vol. 85, No. 12, pp. 8060-8073, June, 1999.

 

JH-2 float glass references

 

Holmquist, T.J., Johnson, G.R., Grady, D.E., Lopatin, C.M., and Hertel, E.S., "High Strain Rate Properties and Constitutive Modeling of Glass", 15th International Symposium on Ballistics, pp. 237-244, Jerusalem, Israel, May, 1995.

 

JH model - JH-2 : ceramic data - float glass

 

http://www.osti.gov/bridge/servlets/purl/41367-gD9pD5/webviewable/41367.pdf

 

Richards, M., Clegg, R., and Howlett, S., "Ballistic Performance Assessment of Glass Laminates Through Experimental and Numerical Investigation", 18th International Symposium and Exhibition on Ballistics, pp. 1123-1130, San Antonio, Texas, November, 1999.

 

JH model - JH-2 : ceramic data - float glass

 

http://hsrlab.gatech.edu/AUTODYN/papers/paper089.pdf

 

Cronin, D.S., Bui, K., Kaufmann, C., McIntosh, G., and Berstad, T., "Implementation and Validation of the Johnson-Holmquist Ceramic Material Model in LS-DYNA", 4th European LS-DYNA Users Conference, Ulm, Germany, May, 2003.

 

JH model - JH-2 : ceramic data - AlN, Al2O3, B4C, SiC, float glass, etc.

 

http://www.dynalook.com/european-conf-2003/implementation-and-validation-of-the-johnson.pdf

 

Zhang, X., Hao, H, and Ma, G., "Dynamic Material Model of Annealed Soda-Lime Glass", International Journal of Impact Engineering, Vol. 77, pp. 108-119, March, 2015

 

JH model - JH-2 : ceramic data – float glass

 

https://www.deepdyve.com/lp/elsevier/dynamic-material-model-of-annealed-soda-lime-glass-WkQCdGS6Fm

 

Sincerely,

James M. Kennedy

KBS2 Inc.

October 16, 2925

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